Based on the randomized matrix multiplication of [1]},
the algorithm of [2]} estimates the covariance operator from a sketch of much smaller size. The procedure is summarized in Algorithm REF . Given a full dataset \(\lbrace x_n\rbrace _{n=1}^N\)  and a sampling probability \(\lbrace p_n\rbrace _{n=1}^N\) , it draws with replacement a subsample \(\lbrace \tilde{x}_c\rbrace _{c=1}^C\)  of size \(C\)  from \(\lbrace x_n\rbrace _{n=1}^N\) . Then, the subsampled empirical covariance operator is computed as
\(\widetilde{\mathcal {C} }_{XX} = \frac{1}{C}\sum _{c=1}^C \frac{1}{N\tilde{p}_c}\tilde{x}_c\otimes \tilde{x}_c.\) 
